[Physics] the potential diff of an infinite resistance wire

Question

In my opinion it should be 0 as current through it is 0 but it is also 0 in case of 0 resistance wire Is it 0 in both the cases

Answer 1

What is the potential diff of an infinite resistance wire?

In circuit theory, an infinite resistance 'wire' is an ideal open circuit and there is a corresponding notion of an open-circuit voltage $V_{OC}$

Consider, for example, a cell (or battery) that is not connected to an external circuit. The cell maintains a voltage across its terminals and this voltage is called the open-circuit voltage of the cell.

If one were to place an ideal voltmeter across the cell, the reading would equal $V_{OC}$ since there is no current through an ideal voltmeter just as there is no current through an open circuit.

Then there is the concept of a Thevenin equivalent circuit

Note that there is an infinite resistance 'wire' (open circuit) connected between nodes A and B. There is no current though the open circuit but there is nonetheless a voltage across and this voltage, the open-circuit voltage, is just the Thevenin equivalent voltage $V_{TH}$.

To verify this, place a resistor $R_L$ between the A & B nodes and calculate the voltage across it. You'll find that the voltage is

$$V_{R_L} = V_{TH}\frac{R_L}{R_{TH} + R_L}$$

Now, take the limit as $R_L\rightarrow\infty$ and find that

$$\lim_{R_L\rightarrow\infty} V_{R_L} = V_{TH}$$

So this is an example of how to find the voltage across an infinite resistance 'wire' since, as you point out, the current through is zero: replace the 'wire' with a resistor $R$, calculate the voltage across the resistor (leave $R$ as a variable) and take the limit as $R\rightarrow\infty$